Optimal Resource Allocation and EE-SE Trade-Off in Hybrid Cognitive Gaussian Relay Channels

Recent literature has suggested the benefits of integrating licensed radio and cognitive radio into a hybrid cooperative communication system. The fundamental properties of such hybrid systems, however, have not been thoroughly investigated. This paper studies the hybrid cognitive Gaussian relay channel (HCGRC), which uses licensed radio resource (RR) and cognitive/unlicensed RR for forward and relay transmissions, respectively. HCGRC fundamentally differs from conventional relay channels in that the licensed and cognitive RRs are not subject to a total resource constraint and that the cognitive RR is opportunistic in nature. With respect to both the upper and lower bounds, we derive the optimal power-bandwidth allocation strategies for the cognitive relay to maximize the capacity, spectrum efficiency (SE), and energy efficiency (EE). The Pareto-optimal EE-SE tradeoff curve is also derived analytically. Our study leads to two key observations. First, the multi-objective power-bandwidth allocation problem is characterized by five regions, each representing a unique performance tradeoff. Second, the reliability of cognitive RR has no impact on the EE-SE tradeoff given unlimited bandwidth and power.